Robust Eulerian-on-Lagrangian Rods

This paper introduces a method to simulate complex rod assemblies and stacked layers with implicit contact handling, through Eulerian-on-Lagrangian (EoL) discretizations.
Previous EoL methods fail to handle such complex situations, due to ubiquitous and intrinsic degeneracies in the contact geometry, which prevent the use of remeshing and make simulations unstable. We propose a novel mixed Eulerian-Lagrangian discretization that supports accurate and efficient contact as in EoL methods, but is transparent to internal rod forces, and hence insensitive to degeneracies. By combining the standard and novel EoL discretizations as appropriate, we derive mixed statics-dynamics equations of motion that can be solved in a unified manner with standard solvers. Our solution is simple and elegant in practice, and produces robust simulations on large-scale scenarios with complex rod arrangements and pervasive degeneracies. We demonstrate our method on multi-layer yarn-level cloth simulations, with implicit handling of both intra- and inter-layer contacts.